We may infer from modern similar experiences that some synagogues were more hellenized and some were more "conservative" and kept the Hebrew. The ones that read in Hebrew certainly did not understand it, just like those parishes which hold liturgies in old languages. But, as we see now, that wouldn't avoid the possibility it happened.
But since the question is what Jesus did, we have two strong evidence that *He* used the Septuaginta: 1) the vast majority of what His disciples and follower wrote was in Greek. They were probably following His lead in this. Had Jesus used Hebrew, we would hardly see His followers who were also Jews resorting to Greek to write anything; 2) Most of the quotes are from the Septuaginta, yet some Hebrew words are used now and then. What this shows is that if Jesus had used the Hebrew text, the followers would not be ashamed of quoting Hebrew sources if necessary. That they used the Greek source suggests they were probably trying to quote as precisely as possible, that is, using the same text He used.
I dunno, I doubt he was reading from the Septuagint in Greek. There were version of the Old Testament in Hebrew at the time, and I really doubt they would have read the OT in Greek in Palestine. They certainly were Hellenized and probably spoke a little Greek, but I would bet it was read in Hebrew.
I don't really think the argument you've presented is very strong at all. Jesus was not speaking to Jews of the diaspora. He was speaking to Jews of the holy land who weren't as strongly hellenized as the Jews of diaspora. The Apostles, on the other hand, were almost entirely writing to Jews of the diaspora. Jews in Greece, Anatolia & Rome. These Jews would have known Greek very well and their access to the scriptures would have been to the Septuagint.
However, as mentioned, Jesus was not part of the diaspora (except for his time in Egypt) and the Jews he was speaking to were not members of the diaspora.
The fact that the Apostles quote from the Septuagint isn't strong evidence for Christ using it. Remember that Christ was reading the scriptures in a synagogue. The Apostles did not have access to synagogues at the time of their writing/dictating the Epistles because they had been thrown out. Therefore they quoted from the Septuagint because they: 1. Were living in and preaching to the diaspora, 2. They didn't have any access to the synagogues, especially the scriptures contained in the synagogues.
Christ may have quoted from or read from the Hebrew versions of the scriptures, but that doesn't mean if he did, the Apostles would have quoted from the Hebrew texts. As I said, the Hebrew texts probably were confined to the synagogues, which the Apostles didn't have access to.
Now I should clarify, that while I'm arguing that Jesus was probably reading the text in Hebrew, that Hebrew text in the synagogue(s) was derived from the Greek Septuagint. So Fabio, you are essentially correct that he was using the Septuagint, but not that he was reading it in Greek, as I would argue it was probably a Hebrew translation from the Septuagint.